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science~life
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Can anyone please give a succinct and clear description on this? I'm a little confused...
HallsofIvy said:(a, b) means "all numbers strictly between a and b". It can also be written as [itex]\{x| a< x< b\}[/itex].
[a, b) means "all numbers strictly between a and b and the number a. It can also be written as [itex]\{x| a\le x< b\}[/itex].
(a, b) means "all numbers strictly between a and b and the number b. It can also be written as [itex]\{ x| a< x\le b\}[/itex].
[a, b] means "all numbers strictlhy between a and b and both the number a and the number b. It can also be written as [itex]\{x| a\le x\le b\}[/itex].
In short, all of these contain the interval between a and b. "[" and "]" mean "include this end point". "(" and ")" mean "do not include this point".
Interval notation is a way to represent a set of numbers within a specific range. It is commonly used in mathematics and is usually written as a combination of brackets and parentheses.
Interval notation is typically written as [a,b] or (a,b), where a and b represent the lower and upper limits of the interval. The brackets indicate that the endpoints are included in the interval, while the parentheses indicate that the endpoints are not included.
In interval notation, a closed interval is represented by square brackets [a,b], which means that both the lower and upper limits are included in the interval. An open interval is represented by parentheses (a,b), which means that the endpoints are not included in the interval.
Yes, interval notation can be used for all types of numbers, including whole numbers, decimals, fractions, and even irrational numbers like pi. It is a versatile and efficient way to represent a wide range of numbers.
Interval notation is helpful in mathematical equations because it makes it easier to express a range of numbers without having to list every single number individually. It also allows for more complex equations to be written more concisely, making them easier to read and understand.